Question 59
Given an integer $n \ge 2$, determine the integral part of the number
$$
\sum_{k=1}^{n-1} \frac{1}{\left(1 + \frac{1}{n}\right) \cdots \left(1 + \frac{k}{n}\right)} - \sum_{k=1}^{n-1} \left(1 - \frac{1}{n}\right) \cdots \left(1 - \frac{k}{n}\right).
$$
$$
\sum_{k=1}^{n-1} \frac{1}{\left(1 + \frac{1}{n}\right) \cdots \left(1 + \frac{k}{n}\right)} - \sum_{k=1}^{n-1} \left(1 - \frac{1}{n}\right) \cdots \left(1 - \frac{k}{n}\right).
$$